Hadeel Mango prepared a derivatives project on Chevron Corporation (CVX) for a course at TAG Graduate School of Business. The document provides a company profile of Chevron, analyzes Chevron stock and option prices, and calculates historical volatility and the risk-free rate. It summarizes Chevron's operations and history, provides examples of Chevron's call and put option prices, and calculates a 0.00015424 risk-free rate and 20.11% historical volatility based on Chevron stock prices from November 17, 2011 to January 0, 2012.

1. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
TAG Graduate School of Business
“Derivatives and Financial Engineering”
Dr. Taher Al-Assaf
Prepared By: Hadeel Mango
Student Number: 2009408053
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2. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
TABLE OF CONTENTS
1. COMPANY PROFILE ...................................................................... 1
2. CHEVRON CORPORATION OPTIONS ............................................. 4
3. RISK FREE CALCULATION .............................................................. 5
4. HISTORICAL VOLATILITY ............................................................... 6
5. THEORITICAL STOCK PRICES ......................................................... 7
6. IMPLIED VOLATILITY ..................................................................... 9
7. OPTION STRATIGIES ................................................................... 10
8. FUTUERS ..................................................................................... 17
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CHEVRON CORPORATION - CVX
HADEEL MANGO
1. Company profile
Business
Chevron is one of the world's leading integrated energy companies, with subsidiaries that
conduct business worldwide. Our success is driven by our people and their unrelenting focus
on delivering results the right way—by operating responsibly, executing with excellence,
applying innovative technologies and capturing new opportunities for profitable growth. We
are involved in virtually every facet of the energy industry. We explore for, produce and
transport crude oil and natural gas; refine, market and distribute transportation fuels and
lubricants; manufacture and sell petrochemical products; generate power and produce
geothermal energy; provide energy efficiency solutions; and develop the energy resources of
the future, including biofuels.
Businesses work in concert to provide the energy that drives human progress. Explore
Chevron’s companies to learn how we use global resources, determination and ingenuity to
meet today’s complex energy challenges.
 Chevron was the first major integrated energy company to offer domestic partner
benefits to our employees.
 In 2010, for the seventh consecutive year, Chevron was given a perfect score on the
Corporate Equality Index by the Human Rights Campaign and was recognized as one
of the Best Places to Work for Lesbian, Gay, Bisexual and Transgender Equality. The
Corporate Equality Index rates nearly 600 businesses on their policies, practices and
diversity efforts relating to lesbian, gay, bisexual and transgender employees,
consumers and investors.
 In 2010, DiversityBusiness.com named Chevron one of America's Top Organizations
for Multicultural Business Opportunities.
 In 2010 and for the eighth consecutive year, the Women's Business Enterprise
National Council honored Chevron as a Top Corporation for providing opportunities
to women entrepreneurs—a tribute to our Supplier Diversity/Small Business
program.
 Profiles in Diversity Journal presented Chevron with its 2010 Diversity Leader Award
for communicating the company's commitment to diversity and for sharing diversity
best practices.
Company Roots
Our company has a long, robust history, which began when a group of explorers and
merchants established the Pacific Coast Oil Co. on Sept. 10, 1879. Since then, our company's
name has changed more than once, but we've always retained our founders' spirit, grit,
innovation and perseverance.
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CHEVRON CORPORATION - CVX
HADEEL MANGO
Over the years, we joined with other companies, each with their own history, strengths and
character. We've grown from a San Francisco-based company with a five-state market in the
Western United States to a major corporation whose subsidiaries conduct business
worldwide. Throughout, we've retained our fundamental purpose: to provide the energy
people need to fuel human progress.
We trace our beginnings to an 1879 oil discovery at Pico Canyon, north of Los Angeles, which
led to the formation of the Pacific Coast Oil Co. That company later became Standard Oil Co.
of California and, subsequently, Chevron. We took on the name Chevron when we acquired
Gulf Oil Corp. in 1984, nearly doubling our worldwide proved oil and gas reserves. Our
merger with Gulf was at that time the largest in U.S. history.
Another major branch of the family tree is The Texas Fuel Company, formed in Beaumont,
Texas, in 1901. It later became known as The Texas Company and eventually Texaco. In
2001, our two companies merged. The acquisition of Unocal Corporation in 2005
strengthened Chevron's position as an energy industry leader, increasing our crude oil and
natural gas assets around the world.
Global Scope
Our diverse and highly skilled global workforce consists of approximately 58,000 employees
and about 4,000 service station employees.
In 2010, Chevron produced 2.763 million barrels of net oil-equivalent per day, 2 percent
higher than in 2009. About 75 percent of that volume occurred outside the United States.
Chevron had a global refining capacity of more than 2 million barrels of oil per day at the
end of 2010.
Our marketing network supports retail outlets on six continents. And we have invested in 13
power-generating facilities in the United States and Asia.
Technology and Emerging Energy
Technology is propelling our growth. We're focusing on technologies that improve our
chances of finding, developing and producing crude oil and natural gas.
We also are investing in the development of emerging energy technologies, such as finding
better ways to make nonfood-based biofuels, integrating advanced solar technology into our
operations and expanding our renewable energy resources.
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5. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
Environment and Safety
As a company and as individuals, we take great pride in contributing to the communities
where we live and work.
We also care about the environment and are proud of the many ways in which our
employees work to safeguard it.
Our persistent efforts to improve on our safe work environment continue to pay off. In 2010,
Chevron achieved our safest year ever, setting new safety records in the days-away-from-
work performance in both Upstream and Downstream operations.
Our Work
We recognize that the world needs all the energy we can develop, in every potential form.
That's why our employees work daily to find newer, cleaner ways to power the world.
Chevron Corporation, through its subsidiaries, engages in petroleum, chemicals, mining,
power generation, and energy operations worldwide. It operates in two segments, Upstream
and Downstream. The Upstream segment involves in the exploration, development, and
production of crude oil and natural gas; processing, liquefaction, transportation, and
regasification associated with liquefied natural gas; transportation of crude oil through
pipelines; and transportation, storage, and marketing of natural gas, as well as holds interest
in a gas-to-liquids project. The Downstream segment engages in the refining of crude oil into
petroleum products; marketing of crude oil and refined products primarily under the
Chevron, Texaco, and Caltex brand names; transportation of crude oil and refined products
by pipeline, marine vessel, motor equipment, and rail car; and manufacture and marketing
of commodity petrochemicals, plastics for industrial uses, and fuel and lubricant additives. It
also produces and markets coal and molybdenum; and holds interests in 13 power assets
with a total operating capacity of approximately 3,100 megawatts, as well as involves in cash
management and debt financing activities, insurance operations, real estate activities,
energy services, and alternative fuels and technology business. Chevron Corporation has a
joint venture agreement with China National Petroleum Corporation. The company was
formerly known as ChevronTexaco Corp. and changed its name to Chevron Corporation in
May 2005. Chevron Corporation was founded in 1879 and is based in San Ramon, California.
Details
Index Membership: Dow Jones Composite
Dow Industrials
Sector: Basic Materials
Industry: Major Integrated Oil & Gas
Full Time Employees: 62,000
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6. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
2. Chevron Corporation Options
Chevron Corporation Common Stock (CVX)-NYSE
Chevron Corporation has various figures of calls and puts options with different expiation
and exercise prices; total options observed were totaling 148 calls and puts options, 38 of
these options were LEAPS with more than 1 year expiration.
The table below is a sample of Chevron Corporation options with different expiration and
exercise prices
Expiration date 16-Dec 12-Jan 12-Mar 12-Jun 13-Jan 14-Jan
Exercise Price (47.5-145) (35-155) (47.5-150) (47.5-145) (47.5-155) (80-130)
number of 25 35 26 24 27 11
options
Options cycle
Stock options can belong to one of three expiration cycles. In the first cycle, the JAJO cycle,
the expiration months are the first month of each quarter - January, April, July, and October.
The second cycle, the FMAN cycle, consists of expiration months February, May, August and
November. The expiration months for the third cycle, the MJSD cycle, are March, June,
September and December.
Chevron Corporation options belongs to January Cycle – (January 2012, February 2012,
March 2012, June 2012).
Chevron Corporation has LEAPS listed for trading which expire in January.
Odd exercise prices
Generally the strike price of options formulated as the following
 If the stock price is higher than $100, the strike price is in the intervals of 10, i.e.:
$100, $110, $120...etc
 If the stock price ranges from $25 to $100, it is in the intervals of 5, i.e. $25,
$30..., $50, $55, $60..., $90, $95.
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7. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
 If the stock price is lower than $25, it is in the intervals of 2.5, i.e. $17.7, $20 and
$22.5.
Data observed from CBOE for Chevron Corporation shows that the exercise price has two
different intervals which is 5 or 2.5 for examples in the intervals of 5 the price trends as
35$, 40$, 45$ and in the intervals of 2.5 the price trends as 92.5$, 95$, 97$ Moreover
Chevron Corporation has no odd prices .
3. Risk free rate calculation
In reference to the Wall Street website the treasury bills bid and ask rates was as follows:
maturity Bid ask Average Remaining Return Compounded
period Return
16 March 0.025 0.005 0.015 (71/360) 0.00003 0.00015424
2012
To find an estimate of the T-bills rate which expired in March 16, we do the
following:
 Calculate the average of the bid and ask discounts, (0.025 + 0.005)/2 =
0.015.
 Then calculate the discount from par value, 0.015 (71/360) = 0.0029583
using the fact that the option has 75 days until maturity. Thus, the price is
100 - 0.0029583 = 99.9970
 Yield on our T-bills equals, (100-99.9969)/99.9969 =0.00003
 The compounded return for a full year would be,
(1.00003)^365/75 – 1 = .00015424. Thus we would use 0.00015424 percent as
our proxy for the risk free rate for the option expiring on 16/03/2012.
4. Historical volatility
Historical volatility calculation is based on the company’s historical closing stock price which
is extracted from Yahoo Finance for the following period 17/11/2011 to 0/01/2012.First we
take a sample of returns on the stock over the past period. We convert these returns into
continuously compounded returns. Then, we compute the standard deviation of the
continuously compounded returns.
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8. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
Stock return calculation is based on the adjusted daily closing prices in order to incorporate
the distributed dividend. The below table shows the company stock historical prices, returns
and the continuously compounded returns:
Continuously
Simple Rate of
Date Open High Low Close Volume Adj Close Compounded
Return
Rate of Return
17/11/2011 100.75 102.13 98.75 100.08 11794300 100.08 NA NA
18/11/2011 100.52 101.5 97.52 97.88 13668700 97.88 -2.20% -2.22%
21/11/2011 96.92 96.94 94.45 95.66 15021100 95.66 -2.27% -2.29%
22/11/2011 95.68 97.25 95 96.42 8939500 96.42 0.79% 0.79%
23/11/2011 95.42 95.58 93.75 93.75 11665200 93.75 -2.77% -2.81%
25/11/2011 94.03 94.45 92.29 92.29 5257300 92.29 -1.56% -1.57%
28/11/2011 96.03 96.35 95 95.77 8403100 95.77 3.77% 3.70%
29/11/2011 95.96 98.05 95.75 97.39 8845100 97.39 1.69% 1.68%
30/11/2011 100.5 102.82 100.11 102.82 13373200 102.82 5.58% 5.43%
01/12/2011 102.82 103 100.96 101.83 7007200 101.83 -0.96% -0.97%
02/12/2011 103.04 103.19 101.5 101.69 6638100 101.69 -0.14% -0.14%
05/12/2011 103.58 104 102.04 102.82 6121800 102.82 1.11% 1.11%
06/12/2011 103.1 104.73 102.84 104.36 7445000 104.36 1.50% 1.49%
07/12/2011 104.22 105.74 103.97 104.52 10323300 104.52 0.15% 0.15%
08/12/2011 104 104.8 101.95 102.25 7720100 102.25 -2.17% -2.20%
09/12/2011 102.74 104.5 102.71 104.25 6624100 104.25 1.96% 1.94%
12/12/2011 104.02 104.23 101.5 103.07 7595800 103.07 -1.13% -1.14%
13/12/2011 104.22 105.89 103.1 103.62 8990000 103.62 0.53% 0.53%
14/12/2011 102.75 104.02 99.51 100.53 15512100 100.53 -2.98% -3.03%
15/12/2011 101.23 101.6 99.32 99.67 9667000 99.67 -0.86% -0.86%
16/12/2011 100.32 100.86 99.59 100.86 14709700 100.86 1.19% 1.19%
19/12/2011 101.16 101.33 99.5 99.72 5977400 99.72 -1.13% -1.14%
20/12/2011 101.94 103.85 101.78 103.67 7278600 103.67 3.96% 3.88%
21/12/2011 103.68 105.53 103.55 105.43 8156600 105.43 1.70% 1.68%
22/12/2011 105.51 106.58 105.06 106.31 7483800 106.31 0.83% 0.83%
23/12/2011 106.63 107.61 106.1 107.5 3779400 107.5 1.12% 1.11%
27/12/2011 107.26 108.49 107.26 107.98 4136200 107.98 0.45% 0.45%
28/12/2011 107.86 108.16 105.88 105.96 5307900 105.96 -1.87% -1.89%
29/12/2011 106.38 107.56 106.32 107.47 4468500 107.47 1.43% 1.42%
30/12/2011 106.79 107.5 106.18 106.4 5009400 106.4 -1.00% -1.00%
03/01/2012 108.74 110.99 108.73 110.37 11518700 110.37 3.73% 3.66%
04/01/2012 109.83 110.37 109.2 110.18 8019100 110.18 -0.17% -0.17%
05/01/2012 109.39 109.54 107.97 109.1 7184900 109.1 -0.98% -0.99%
Standard Diviation 2.07%
Annualized SD 25.02%
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9. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
5. Theoretical Stock Prices
As of January 05, 2012, Chevron Corporation stock price was $109.10, the table below
shows three options which has been selected in order to illustrate the required three states:
in the money, at the money and out of the money
The chosen exercise prices as follows, $ 105, $110, and$ 115. For the $105 price it’s
considered in the money for the call option and out of the money for the put option. $110
considered out of the money for both call and put options, and $110 considered out of the
money for both call and put options.
Call Put Call Put
MARCH - 2012 MARCH - 2012 MARCH - 2012 MARCH - 2012
exercise price
Theoretical Price Actual Price
100 11.27 2.69 10.72 2.22
111 5.59 7.08 3.50 5.80
120 2.37 13.88 0.60 12.45
Comparing theoretical prices to actual prices we found that they are overpriced in
accordance to actual option prices at exercise date March 16th 2012.
In reference to black and Scholes formula, and the binomial model based on 1000 step the
calculated theoretical price and the calculation process for each of the above mentioned
exercise prices represented below:
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CHEVRON CORPORATION - CVX
HADEEL MANGO
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CHEVRON CORPORATION - CVX
HADEEL MANGO
6. Implied Volatility
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CHEVRON CORPORATION - CVX
HADEEL MANGO
Comparing the volatility to the implied volatilities calculated by Black - Scholes - Merton
implied volatility function for the selected exercise prices, it is found that the implied
volatilities are near the range of 25% with a normally distributed observations that have
variances between ( -5, +5) and they were as follow:
Exercise Price Call Implied Volatility Put Implied Volatility
100 25.57% 30.60%
110 20.40% 28.15%
120 18.68% 27.30%
7. Options Strategies
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CHEVRON CORPORATION - CVX
HADEEL MANGO
In Order to Investors to keep their investments save and have the minimum losses, they
can hedge themselves by using different strategies . by Using option TOOL box .We will
applied strategies on Alcoa’s options.
Investors used to use different options strategies in order to hedge their positions
and maintain minimum risk.
Some of these strategies are bull spread, bear spread, collars, butterfly, calendar,
and straddle.
Assuming the value of the stock was 109.1, volatility 25, and risk free rate =1 (as it is the
lowest number on tool box).
Bull Spread Strategy:
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CHEVRON CORPORATION - CVX
HADEEL MANGO
The Bull spread strategy consist of the purchase of the option with the lower
exercise price and the sale of option with higher exercise price, the chosen
exercise price were $100 and $115 with MARCH Expiration.
March Maturity
Bull Spreads long call with $100 exercise price
short call with $115 exercise price
The figure represented above illustrates the bull spread strategy for Chevron Corporation
March $100 and $115 calls with premiums of $10.72 and $1.45 the red line is the long
position of March $100.
Bear Spread Strategy:
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15. DERIVATIVES PROJECT
CHEVRON CORPORATION - CVX
HADEEL MANGO
The bear spread strategy consists of purchase or (long) of the high exercise price put and
sell or (short) of the low exercise price put, the chosen exercise price were $100 and $115
with March expiration.
March Maturity
Bear Spreads long Put with $115 exercise price
short Put with $100 exercise price
The above figure illustrates the Put Bear Spread for Chevron Corporation March $115 and
$100 puts with premiums of $2.22 and $8.80, respectively the yellow line is long position in
the $115 put.
Collars Strategy:
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CHEVRON CORPORATION - CVX
HADEEL MANGO
Collars is a strategy in which the holder of position in a stock buys a put with an exercise
price lower than the current stock price and sells a call with an exercise price higher than
the current stock price . The call premium is intended to reduce the cost of the put
premium .the call premium is often set to make the call premium completely offset the
put premium as follows:
March Maturity
Collars long Put with $100 exercise price
short call with $115 exercise price
The above figure illustrates the collar for Chevron Corporation March $100/$115 where the
trader bought the put option with exercise price of $100 and premium of $2.22 and sold a
call option with exercise price of $115 and premium of $1.54.
Butterfly Spreads
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CHEVRON CORPORATION - CVX
HADEEL MANGO
A butterfly spread, sometimes called a sandwich spread, is a combination of a bull spread
and a bear spread. However, this transaction involves three exercise prices: X1, X2 and X3
where X2 is half way between X1 and X3. Hence, we construct a call bull spread by
purchasing the call with the low exercise price X1 and writing the call with the middle
exercise price X2. Then we also construct a call bear spread by purchasing the call with high
exercise price X3 and writing the call with the middle exercise price X2. This strategy is
followed if our expectation on the stock price will be stable with no changes in price.
The table below represents the chosen exercise prices and the butterfly strategy.
March Maturity
Butterfly long call with $100 exercise price
short two calls with $110 exercise price
Long call with $115 exercise price
The below figure illustrate the butterfly spread for the March $100, $110 and $115 calls
with premium of $10.72, $3.50 and $1.54. The maximum profit is obtained when the stock
price at expiration is at the middle exercise price. Generally the butterfly spread strategy
assumes that the stock price will fluctuate very little.
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CHEVRON CORPORATION - CVX
HADEEL MANGO
Calendar Spreads strategy
A calendar spread, also known as a time spread or horizontal spread, involves the purchase
of an option with one expiration date and the sale of another identical option with a
different expiration date.
Exercise price of $110
Calendar long call with March expiration
short call with June expiration
The profitability of the calendar spread is determined by the difference in the option time
values, the longer term call will have more time value.
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CHEVRON CORPORATION - CVX
HADEEL MANGO
Straddle Strategy
A straddle is the purchase of a call and a put that have the same exercise price and
expiration date. By holding both a call and a put, the trader can capitalize on stock price
movements in either direction. This strategy is followed if our expectation on the stock price
will not to be stable and it will changes either by increasing or decreasing mode.
Exercise price of $110
Straddle long call with March expiration
long put with March expiration
The figure illustrates the straddle for Chevron Corporation March $110 options. As noted
the straddle is designed to capitalize on high stock price volatility in order to create a
profit the price must move substantially in either direction.
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CHEVRON CORPORATION - CVX
HADEEL MANGO
8. Comparison of the Futures Price of the stock with Theoretical
Fair Value
Chevron Corporation has four expiration periods for their future contracts, which are
January, February, March and June. In order to calculate the theoretical fair value for
March future contract first we need to calculate the risk free rate for March treasury bills
as previously obtained from the Wall Street Journal and the following are March treasury
bills calculations:
Risk Free Calculation
Maturity Bid Asked Change Asked yield
22nd March 2012 0.020 0.010 -0.0050 0.0100
29th March 2012 0.015 0.005 0.0000 0.0050
(Bid+ Ask)/2 0.015
A*(71/360) 0.0029583
100-B 99.9970
(100-C)/C 0.00003
((1+D)^(365/71))-1 0.00015424
 Future theoretical fair price
From the table above the observed risk free rate was 0.00015423, since the price of
Chevron Corporation stock today 05/01/2012 is $109.1, the calculated theoretical fair
future price for March is 108.3068 which is almost equal to the stock price, and the
calculation is shown below:
F = P ∙ (1 + r) – Div
F= $109.1 *(1+0.00015424) – 0.8100
F= 108.3068
Comparing theoretical price with the market price, we will found that the theoretical price is lower
than the market price by 0.1932 based on the above information it is recommend to sell the stock.
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